go to any automotive store and they will have 1/4" crimp on connectors like this in a kit with some pliers and other connectors, get one of those(around 12 USD) and youll have all you need. Just strip the wire a bit 1/4" or so, slide it into the approprate sized connector and crimp it with the pliers.
A car battery CAN supply 200+amps of power when short circuted. However your alternator on your car cannot! just for a refrence an 300W inverter will pull ~30 amps at full draw and your ALT should be able to handel this without much dificulty.